The local Health Department conducted a study in 2009 of 900 adults asking each adult the number of times they wash their hands per day. The mean number of times those sampled washed their hands was 7.946 with a standard deviation of 6.567. Researchers would like to include a 90% confidence interval.How many degrees of freedom would be associated with this t-distribution? With 90% confidence, we estimate the mean number of times an individual washes their hands is between and . Enter the lower limit in the first box and the upper limit in the second box. (The appropriate t critical point is t=1.65. Round the limits of your interval to 4 decimal places.)Based on the interval computed, can we conclude that the mean number of times local adults wash their hands is more than 8 times per day

Name: The local Health Department conducted a study in 2009 of 900 adults as
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Description: The local Health Department conducted a study in 2009 of 900 adults asking each adult the number of times they wash their hands per day. The mean number of times those sampled washed their hands was 7.946 with a standard deviation of 6.567. Researche

Given Information: Sample size (n) = 900 Sample mean (x¯) = 7.946 Standard deviation = 6.567…

Answered: The local Health Department conducted a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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The local Health Department conducted a study in 2009 of 900 adults asking each adult the number of times they wash their hands per day. The mean number of times those sampled washed their hands was 7.946 with a standard deviation of 6.567. Researchers would like to include a 90% confidence interval.

How many degrees of freedom would be associated with this t-distribution?
With 90% confidence, we estimate the mean number of times an individual washes their hands is between and . Enter the lower limit in the first box and the upper limit in the second box. (The appropriate t critical point is t=1.65. Round the limits of your interval to 4 decimal places.)
Based on the interval computed, can we conclude that the mean number of times local adults wash their hands is more than 8 times per day

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Step 1

Given Information:

Sample size (n) = 900

Sample mean ( $\bar{x}$ ) = 7.946

Standard deviation = 6.567

Degrees of freedom = $n - 1 = 900 - 1 =$ 899

To construct 90% Confidence Interval for population mean:

Confidence Interval is obtained using the formula:

$C . I = \bar{x} \pm t * (\frac{s}{\sqrt{n}})$

where, t* is the t-critical value at 90% Confidence Interval and degrees of freedom 899.

s is the standard deviation.

Since, sample size n is greater than 30 t* values are closer to Z-critical values.

t* = 1.65 (given)

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